Field of the Invention
The present invention relates to a storage medium, an information processing apparatus, and a calculation method, and particularly to a rendering expression technique for radiance that occurs in an object surface due to a light source.
Description of the Related Art
In recent years, in the field of computer graphics, various rendering expression techniques have been proposed and implemented in order to provide high quality and realistic graphics. One such rendering expression technique renders/reproduces a radiance that occurs due to a light source considering a material of an object (a rendering object) that is to be rendered, a light source type of an illumination which is arranged in the periphery of the object, or the like.
A radiance at a single point (a shading point) on a rendering object or a radiance on a single pixel on an image that is to be rendered is reproduced by summing the radiances that occur due to illumination (direct light) arranged in the periphery, and due to so-called indirect light which occurs by those light sources reflecting from particular surfaces. More specifically, a solution (the radiance due to each light source) to a rendering equation for each light source is obtained, and by integrating these, the radiance at a shading point due to the peripheral light sources is calculated. As one approach to obtaining this integration solution, for the indirect light, there exists an instant radiosity approach for approximating the indirect light from a plurality of virtual point lights. Also, regarding the direct light, there is an approach for obtaining an approximation solution for the integration by approximating a light source that has an area by a plurality of point light sources.
Meanwhile, in a scheme for simply approximating point light sources as described above, when the light source position and the shading point are extremely close, the shading point is of a material that shows a sharp reflection distribution as with a specular reflection, or the like, there are cases in which unnatural rendering results (a spike-form artifact) such as the shading point suddenly becoming bright are shown. This is due to a dispersion of an error becoming large when an item indicating the distance to the shading point exists in the denominator in the rendering equation, and a bidirectional reflection distribution function (BRDF) existing in the numerator is sharp.
In response to this, in Jiaping Wang et al., “All-Frequency Rendering of Dynamic, Spatially-Varying Reflectance”, ACM Transactions on Graphics, Vol. 28 Number. 5, pp. 133:1-133:10, December, 2009, by approximating to a spherical Gaussian (SG approximating) a light source, occurrences of unnatural specular reflections in a scene that defines Spherical Light having a small radius as the direct light are eliminated.
However, because the approximation solution approach of the rendering equation that Wang et al. proposed ignores physics, tuning of parameters depending on the scene is necessary for each light source, and there are cases in which this is not realistic when there exist many light sources, or the user work corresponding to the tuning is cumbersome. Also, because Wang assumes only Spherical Light with a small radius, there is the possibility that energy will not conserved and the approximation error will be large due to the radius becoming large in this solution. Furthermore, because the distance between the light source and the shading point exists in the denominator in the rendering equation after the approximation, there are cases in which a spike-form artifact still appears in the rendering result.
Meanwhile, in an approach proposed in Kun Xu et al., “A Practical Algorithm for Rendering Interreflections with All-frequency BRDFs”, ACM Transactions on Graphics, Vol. 33 Number. 1, pp. 10:1-10-16, January, 2014, an SG approximation is performing for a cone formed by a shading point and a light source (a virtual spherical light source) considering the conservation law of energy, but when the distance between the light source and the shading point is short, avoiding the occurrence of a spike-form artifact is impossible, and so different approaches are used in accordance with the distance.